Phase diagram, polymer solutions

Keywords Modeling Mixed solvents Phase diagrams Polymer solutions Ternary mixtures Thermodynamics... 

Fig. 3. Phase diagram for solutions of poly-p-benzamide in dimethyl acetamide/lithium chloride I0). Polymer inherent viscosity 1.18...

Fig. 1.10. Cooling curves (a) and a portion of the diagram of state (b) of HDPE-vacuum oil system L, a and j3 - zones of liquid phase existence (melt), solid solutions of PE in oil and oil in PE, respectively L +/3, a - - / - zones of coexisting liquid phase, solid solution and two solid solutions Li- - L2 - stratification zone of two liquid phases (saturated polymer solution in oil and vice versa) ELC and ENC - liquids and solids lines...

KR1 Krause, C. and Wolf, B.A., Shear effects on the phase diagrams of solutions of highly incompatible polymers in a common solvent. 1. Equilibrium behavior and rheological properties, MflCTOiMo/ecM/es, 30, 885, 1997. 

The phase diagrams of solutions can be calculated by the statistical thermodynamics of lattice models [29]. The lattice model of polymer solutions was first considered by Chang [30] and Meyer [31]. The well-known Flory-Huggins equation was then successfully derived by Flory [32,33] and Huggins [34] to deal with the solutions of flexible polymers by using a mean-field approximation. 

Fig. 10. Modeling of phase diagrams for solutions of the polymers A and B in a common solvent by analogy the procedure described for polymer solutions in mixed solvents. Simplicity (left) and con-non-solvency (right)...

Phase Diagrams in Solutions oT Rigid Rod-Like Polymers... 

Figure 2 Schematic phase diagram for solutions of a molecularly uniform polymer. Polymer-lean phase (sol) A, stable B, metastable and C, unstable, segregation of a gel phase. Polymer-rich phase (gel) D, stable E, metastable and F, unstable, segregation of a sol phase. Reproduced from Derham, K. W. Goldsbro, J. Gordon, M. PureAppl. Chem. 1974, 38, 97. International Union of Pure and Applied Chemistry.

M. Watzlawek, H. Lowen, C. N, Likos. Phase diagram of star polymer solutions (submitted for pubhcation, 1999). 

The hydrophobic interaction results in the existence of a lower critical solution temperature and in the striking result that raising the temperature reduces the solubility, as can be seen in liquid-liquid phase diagrams (see Figure 5.2a). In general, the solution behaviour of water-soluble polymers... 

Temperature-sensitive polymers, depending on polymer structure and polymer-polymer interactions, generally exhibit two behaviors, lower critical solution temperature (LCST) [31] and upper critical solution temperature (UCST). Phase diagrams for these behaviors are presented in Figure 9. 

Figure 9 Qualitative phase diagram of a polymer solution showing phase separation both on heating (at the lower critical solution temperature) and on cooling (at the upper critical solution temperature). (From Ref. 31.)...

Based on the analogy between polymer solutions and magnetic systems [4,101], static scaling considerations were also applied to develop a phase diagram, where the reduced temperature x = (T — 0)/0 (0 0-temperature) and the monomer concentration c enter as variables [102,103]. This phase diagram covers 0- and good solvent conditions for dilute and semi-dilute solutions. The latter will be treated in detail below. 

The melting point Tm is computed by solving this equation iteratively. It is often convenient to use Ec/(kBTm) as our unit of (inverse) temperature. The phase diagram of the polymer solution then depends on the molecular parameters r, q, B/Ec, and Ep/Ec, the composition parameters n and 2, and on the temperature parameter Ec/(kBTm). 

When B is positive, the polymer solution can exhibit liquid-liquid demixing. By adjusting the relative values of B and Ep, we can tune the phase diagrams of polymer solutions and study the interplay of freezing, on the one hand, and demixing on the other [14]. 

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